Question

Simplify the radical expression... r7 (r14 + r3)

Answer 1

\[\sqrt{7} (\sqrt{14} + \sqrt{3})\]

Answer 2

distribute the roots. Remember though:\[ \sqrt{a} \times \sqrt{b} = \sqrt{ab}\]

Answer 3

so would it be \[\sqrt{14 * 7} + \sqrt{3*7}\] ? I suck at this so........ I could be way off

Answer 4

Yes. You're correct. Don't 4get to simplify.

Answer 5

\[\sqrt{98} + \sqrt{21}\] ?

Answer 6

That's correct, but you didn't need to multiply. Remember: \[\sqrt{14 \times 7} = \sqrt{(7 \times 2) \times 7}\] and remember when you have two of the sane number under a radical you can factor it out.

Answer 7

How do I factor out numbers that's underneath a radical?

Answer 8

You simply take it out. Remember: \[\sqrt{a^2} = \sqrt{a \times a } = a\]
ONLY if you have two of the same numbers or variables.

Answer 9

How would that look with actual numbers?

Answer 10

Can I have an example o.o

Answer 11

Pick any two of the same numbers and multiply them. For instance, \[182 \times 182 = 33124\]
if you take the square root of that: \[\sqrt{33124} = \sqrt{182 \times 182} = 182\]

Answer 12

\[7\times7=49\] \[\sqrt{49} = \sqrt{7 \times 7 } = 49\] .... this doesn't make sense to me >.<

Answer 13

No. Look at my example. What was the final answer when I had 33124?

Answer 14

sqrt182 x 182

Answer 15

Yes. 182 x 182 = 33124
IF i take the square root of 33124 you get 182.

That's because a square root takes factors out numbers in pairs. So notice how 33124 is the same thing as 182 squared. Which means square root of 33124 = 182. Because I had TWO 182's
So your final answer is 182 NOT 33124.
It's basically the reverse of squaring something. Like 7.

7 x 7 = 49.
NOW if I took the square root of 49 you would get 7.
because there are TWO sevens under the radical.

Answer 16

So.............. it would just end up being 7?